Your cat is very obviously unregulated with his thyroid. Most common symptoms of hyperthyroidism are increased appetite (ravenous is what most people usually describe it as), drinking more, urinating more, losing weight (despite eating more) and restlessness. Some cats may even become aggressive. Your cat is exhibiting most if not all of these.
Basically what the hyperactive thyroid does is increase his metabolism. That means that it increases his blood pressure, heart rate and digestion. If it stays uncontrolled for long periods of time it can lead to chronic issues (ie blindness due to the BP being so high and the little vessels in his eyes bursting, heart disease, kidney problems etc).
When it comes to the medication, there is a "maximum" dose in the sense that the company has only tested it up to this dose. Anything beyond this dose hasn't been tested and so no vet can tell you how safe it's going to be to be using long term. At 17, he's likely coming to the end of his natural life anyway, so I'd probably take the risk myself, but ultimately that's a decision for yourself and your vet to make (also up to your vet how comfortable they'd be to increase the dose without bloods and going just on clinical signs).
Being hyperthyroid is not a nice feeling (think constant racing heart and feeling hungry all the time), so I always recommend if you're not going to treat kindest thing is to let them go, as you wouldn't want them to be living like this (plus the risks of all the possible complications I mentioned earlier). So I would recommend a visit to your vet, discuss dose adjustments (with or without bloods, your vet will be the best to help you decide what's best/safest for your cat) and if that's not an option, then yes I would say letting him go is a very valid option.
Best of luck to you and your kitty!